Given a box of coins where exactly half of the coins are fair coins and the other half are loaded coins (phead = 0.9), if you pick one coin from the box and toss it five times, what is the probability to see five heads in a row?
If you randomly pick a coin from the box mentioned above (i.e., half of coins were loaded with phead = 0.9), toss it five times and get five heads. What is the probability that this is a fair coin?
